A simple formula for local burnup based on constant relative reaction rate per nuclei

TL;DR

This paper introduces a simple analytical formula for local burnup and isotope distribution in nuclear fuel, matching Monte Carlo results efficiently and applicable to different conditions with minimal computational effort.

Contribution

It presents a novel, straightforward formula for calculating local burnup and isotope distributions, validated against Monte Carlo simulations and applicable to various neutron penetration scenarios.

Findings

The formula accurately reproduces Monte Carlo results across burnup levels.

Reaction rates are nearly independent of radius, simplifying calculations.

The method is effective for fuel rods in different assembly configurations.

Abstract

A simple and analytical formula is suggested to solve the problems of the local burnup and the isotope distributions. The present method considers two extreme conditions of neutrons penetrating the fuel rod. Based on these considerations, the formula is obtained to calculate the reaction rates of $^{235}$U, $^{238}$U, and $^{239}$Pu and straightforward the local burnup and the isotope distributions. Starting from an initial burnup level, the parameters of the formula are fitted to the reaction rates given by a Monte Carlo (MC) calculation. Then the present formula independently gives very similar results as the MC calculation from the starting to high burnup level, but takes just a few minutes. The relative reaction rates are found to be almost independent on the radius (except $(n,\gamma)$ of $^{238}$U) and the burnup, providing a solid background for the present formula. A more realistic examination is also performed when the fuel rods locate in an assembly. A combination of the present formula and the MC calculation is expected to have a nice balance on the accuracy and the cost on time.